1. Field of the Invention
This invention relates in general to vertical-scanning interferometry (VSI) for surface characterization. In particular, it relates to an error-correction method for the high-definition vertical-scan interferometric (HDVSI) procedure described in Ser. No. 11/473,447, herein incorporated by reference.
2. Description of the Related Art
The well known techniques generally classified as phase-shifting interferometry (PSI) and vertical scanning interferometry (VSI) make it possible to measure the profile of most samples. However, they do not allow low-noise measurement of samples that combine smooth surfaces with large profile gradients and discontinuities. Measuring the profile of such samples requires the large scanning range of VSI (with vertical resolution in the order of 1/100 of a wavelength and scanning range in the order of millimeters), while characterizing a smooth surface texture requires the vertical resolution normally afforded by PSI (in the order of 1/1000 of a wavelength or less).
This problem has been addressed by the development of enhanced VSI algorithms (named EVSI in the art) that combine both PSI and VSI. In particular, Ser. No. 11/473,447 disclosed a new approach (named HDVSI, from high-definition VSI) based on performing a coarse calculation of surface profile with a conventional VSI method such as center of mass (COM), quadrature center of mass (QCOM), or zero crossing detection (ZCD), and concurrently performing a phase calculation carried out using the same irradiance frame data acquired for VSI. However, the phase calculation does not utilize the conventional n-frame phase shifting approach of the prior art. Instead, it utilizes a quadrature-demodulation (QD) algorithm applied to the irradiance data contained in the VSI correlogram.
As a result of this concurrent procedure, the phase calculation is independent of the position of any particular interferometric fringe and, therefore, it is more accurate and its results are more certain than those produced by the combined VSI/PSI methods of the prior art. Once both calculations are accomplished, the phase data are incorporated into the coarse profile data through a unique “unwrapping” method that yields a final surface map with sub-nanometer resolution within a large z-height range.
The HDVSI algorithm decouples the calculation of phase from the calculation of fringe-intensity peak. This results from the fact that QD manipulation of the correlogram data does not require a prior determination of the position of the coherence intensity peak. Therefore, the calculated phase map of the surface does not inherit the errors produced by the calculation of the coarse map. Such errors are removed from the coarse map, prior to combining it with the phase map, by consistently rounding all VSI measurements to an integer multiple of 2π. In other words, the VSI coarse map is rounded to an integer multiple of λ/2. (Typically, the accuracy of a VSI coarse map is much better than λ/2.) As a result, the VSI errors are completely removed from the VSI coarse map through the rounding process, an achievement that is not possible with prior-art approaches. Thus, the HDVSI algorithm allows profiling to sub-nanometer accuracy with conventional equipment, the only necessary changes being in the computational components required to round the VSI data, to implement the QD algorithm, and to combine the phase data with the corrected VSI data in real time, as data are acquired during the scan.
Ideally, the scanner steps and the effective wavelength of the light source are constant and can be determined through precise calibration procedures. However, in reality the scanner position suffers from system errors, such as scanner nonlinearity and random deviations due to mechanical vibrations. Similarly, the effective wavelength of the irradiance produced by light source changes with the slope of the sample surface and also as a result of scanner nonlinearities. Therefore, the scanner sampling step and the effective wavelength are not constant and cause errors that distort the measured sample-surface profile.
A techniques for real-time correction of scanner-nonlinearities is described in a separate disclosure. The present invention is directed at a novel approach for the correction of errors caused by changes in the system's effective wavelength.